Let p be a positive integer and let A((p)) (R, S) be the class of nonnegative integral matrices with entries less than or equal to p, with row-sum partition R, and column-sum partition S. In this paper we state a new necessary and sufficient condition for A((p)) (R, S) not equal empty set. This condition generalizes the well known Gale-Ryser theorem. We also present a canonical construction for matrices in A((p)) (R, S).
- Integral matrices with given lines
- Partition domination